Pc. Dauby et al., HEXAGONAL MARANGONI CONVECTION IN A RECTANGULAR BOX WITH SLIPPERY WALLS, Quarterly Journal of Mechanics and Applied Mathematics, 46, 1993, pp. 683-707
A linear and nonlinear study of surface-tension-driven instability in
a rectangular box with slippery lateral walls is presented. Particular
attention is devoted to steady convection with hexagonal structure. I
t is shown that, even in very small boxes, convection can set in in th
e form of hexagons more or less distorted according to the aspect rati
os of the box. The distorted hexagons appear generally as subcritical
solutions; the depth of the subcritical domain is determined as a func
tion of the Prandtl number. In particular, it is found that, at small
Prandtl numbers (Pr less-than-or-equal-to 0.23), the direction of the
flow may be downwards at the cell centre. For medium to large values o
f the Prandtl number, the fluid rises at the centre of the hexagons, a
s is observed in most experiments.